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Feb 16th, 2012
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  1. using System;
  2. using System.Diagnostics;
  3.  
  4. public class Chall2
  5. {
  6.    
  7.     public static void Main(string[] args)
  8.     {
  9.         int max = int.Parse(args[0]);
  10.         var rand = new Random();
  11.         Stopwatch sw = new Stopwatch();
  12.         sw.Start();
  13.  
  14.         var result = Shuffle( max, n=> rand.Next(n+1) );       
  15.         sw.Stop();
  16.        
  17.         Console.WriteLine(" In : {0} ms", sw.Elapsed.TotalMilliseconds);
  18.  
  19.     }
  20.  
  21.  
  22.     // n: number of slots (shuffles n-1)
  23.     // generator:  a random generator given x that gives 0 <= val <= x    
  24.     private static int[] Shuffle(int n, Func<int, int> generator)
  25.     {
  26.         int[] values = new int[n];     
  27.         values[0] = 0;
  28.         for( int i=1; i < n; i++)
  29.         {
  30.             var pick = generator(i);
  31.             values[i] = values[pick];
  32.             values[pick] = i;
  33.         }  
  34.         return values;
  35.     }
  36.  
  37.     //proof by induction:  Each number is output once, and
  38.     // for each possible sequence of random numbers,
  39.     // a different output sequence is obtained
  40.     //   For n = 2:
  41.     //  Possible random sequence:     Output:
  42.     //          0                       [1,0]
  43.     //          1                       [0,1]
  44.     //   For n =3
  45.     //          0, 0                    [2,0,1]
  46.     //          0, 1                    [1,0,2]
  47.     //          1, 0                    [0,1,2]
  48.     //          1, 1                    [0,2,1]
  49.     //          0, 2                    [1,2,0]
  50.     //      and so on... (left to the reader)
  51.     // Since there are n! possible random sequences, and
  52.     // n! possible shuffles, and each unique random sequence
  53.     // outputs a unique shuffle, every possible shuffle has
  54.     // an equal chance, given an acceptable random generator.
  55. }
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